# Re: RDF Semantics: use of functions IEXT / ICEXT

From: pat hayes <phayes@ai.uwf.edu>
Date: Fri, 28 Feb 2003 12:13:46 -0700
Message-Id: <p05111b11ba8557386af9@[10.0.100.86]>

```
>  >.....
>>>   >>The semantic conditions on rdfs:range and rdfs:domain in Section 3.3
>>>>>do not yet incorporate explicit domain assumptions as just
>>>>>discussed.  It seems that additions such as the following need
>>>>
>>>>axiomatic triples in the next table and the other conditions on range
>>>>and domain.
>>>>
>>>>It is probably easiest to express the reasoning in terms of triples
>>>>that must be satisfied by an interpretation I. For example, suppose
>>>><x,y> is in IEXT(I(rdfs:range)), ie that
>>>>
>>>>I |= (x) rdfs:range (y)
>>>
>>>I do not understand this step.  In these two lines x/y have a different
>>>origin.  In "<x,y> is in IEXT(I(rdfs:range))", x and y are in IR.
>>>In the triple "(x) rdfs:range (y)", x and y are uri's or blank nodes
>>>(y may also be a literal).  So this conclusion ("ie that")
>>>is not clear.
>>
>>Sorry, I was using an unstated convention. Let me rephrase it more
>carefully.
>>
>>Suppose <x,y> is in IEXT(I(rdfs:range)) and suppose that I(aaa)=x and
>>I(bbb)=y. Then
>>
>>I |= aaa rdfs:range bbb .
>>
>>Now, since
>>
>  >I |= rdfs:range rdfs:domain rdf:Property .  (axiomatic triple)
>>
>>it follows by the semantic conditions on rdfs:domain that
>>
>>I |= aaa rdf:type rdf:Property .
>>
>>and hence that I(aaa)=x is in IP.
>>
>>Similarly for bbb, the axiomatic triple defining the range of
>>rdfs:range, and IC.
>>
>>Pat
>
>Pat, thank you for the explanation.
>You now introduce in the proof an additional assumption.

No, this is only an assumption of the way I presented the argument in
the email. Let me rephrase the argument in full without trying to
shorten it:

First, the truth of the axiomatic triple

rdfs:range rdfs:domain rdf:Property .

and the semantic conditions on rdfs:domain together require that

<x,y> inIEXT(I(rdfs:range)) implies x in ICEXT(I(rdf:Property))

which in turn, by applying the condition (definition if you like :)

IP= ICEXT(I(rdf:Property))

means that

<x,y> in IEXT(I(rdfs:range)) implies x in IP

Similarly y is in IC, using a different axiomatic triple.

Is this more convincing?

-Pat

>What you prove is the following:
>   If <x,y> is in IEXT(I(rdfs:range))
>   AND IF x and y are in the range of the function IS
>   then x is in IP and y is in IC.
>However, this statement does not suffice:  the additional
>assumption (AND IF ...) would need to be dropped.
>However, I believe that it is not possible to prove that
>   If <x,y> is in IEXT(I(rdfs:range))
>   then x is in IP and y is in IC
>(and similarly for rdfs:domain).
>
>Therefore, my remark remains.
>Let me recall in a slightly rephrased manner what I said in
>the first mail in this thread:
>
>For each occurrence of IEXT(x) or ICEXT(x), it
>should be clear that x is in the domain of the function
>involved.  (For IEXT, this domain is the set IP.
>For ICEXT, the domain is the set IC, as you have now confirmed.)
>For example, in Section 3.3 the semantic conditions on
>subClassOf and subPropertyOf take care of this explicitly.
>
>The semantic conditions on rdfs:range and rdfs:domain in Section 3.3
>do not yet incorporate explicit domain assumptions as just
>discussed.  It seems that additions such as the following need
>
>   If <x,y> is in IEXT(I(rdfs:range))
>   [then x is in IP and y is in IC] and
>   [if, in addition,] <u,v> is in IEXT(x) then
>   v is in ICEXT(y)
>
>   If <x,y> is in IEXT(I(rdfs:domain))
>   [then x is in IP and y is in IC] and
>   [if, in addition,] <u,v> is in IEXT(x) then
>   u is in ICEXT(y)
>
>>--
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>>
>>
>
>Herman

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40 South Alcaniz St.			(850)202 4416   office
Pensacola              			(850)202 4440   fax
FL 32501           				(850)291 0667    cell
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```
Received on Friday, 28 February 2003 14:13:50 UTC

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